The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Estimating Automobile Insurance Premiums Based on Time Series Regression

시계열 회귀모형에 근거한 자동차 보험료 추정

  • Kim, Yeong-Hwa (Department of Applied Statistics, Chung-Ang University) ;
  • Park, Wonseo (Department of Statistics, Graduate School of Chung-Ang University)
  • 김영화 (중앙대학교 응용통계학과) ;
  • 박원서 (중앙대학교 대학원 통계학과)
  • Received : 2012.10.12
  • Accepted : 2013.02.11
  • Published : 2013.04.30
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Abstract

An estimation model for premiums and components is essential to determine reasonable insurance premiums. In this study, we introduce diverse models for the estimation of property damage premiums(premium, depth and frequency) that include a regression model using a dummy variable, additive independent variable model, autoregressive error model, seasonal ARIMA model and intervention model. In addition, the actual property damage premium data was used to estimate the premium, depth and frequency for each model. The estimation results of the models are comparatively examined by comparing the RMSE(Root Mean Squared Errors) of estimates and actual data. Based on real data analysis, we found that the autoregressive error model showed the best performance.

보험료 및 보험료 구성요소에 대한 예측모형은 합리적인 보험료 결정에 필수적이다. 본 연구에서는 가변수 회귀모형, 독립변수 추가모형, 자기회귀 오차모형, 계절형 ARIMA 모형, 개입모형 등 적정한 자동차 대물 손해보험료 추정에 사용되는 다양한 모형을 소개하였다. 또한 실제 자동차 대물 보험료 자료를 이용하여 각 모형을 이용하여 보험료, 심도, 빈도 등을 추정하였으며, 모형의 추정결과는 추정치와 실제 자료값의 차이에 근거한 RMSE(Root Mean Squared Errors) 값을 통해 비교하였다. 실제 자료 분석 결과, 자기회귀 오차모형이 가장 좋은 성능을 보여주는 것을 알 수 있었다.

Keywords

References

  1. Box, G. E. P and Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems, Journal of the American Statistical Association, 65, 70-79.
  2. Cho, S. and Sohn (2009). Time Series Analysis using SAS/ETS, Yulgok Press, Seoul.
  3. Cummins, J. A. and Powell, A. (1980). The performance of alternative models for forecasting automobile insurance paid claim costs, ASTIN Bulletin, 11, 91-106. https://doi.org/10.1017/S0515036100006681
  4. Diebold, F. X. and Mariano, R. S. (1995). Comparing predictive accuracy, Journal of Business and Economic Statistics, 13, 253-263.
  5. Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, 427-431.
  6. Durbin, J. and Watson, G. (1950). Testing for serial correlation in lest squared regression I, Biometrika, 37, 409-428.
  7. Durbin, J. and Watson, G. (1951). Testing for serial correlation in lest squared regression II, Biometrika, 38, 159-178. https://doi.org/10.1093/biomet/38.1-2.159
  8. Durbin, J. and Watson, G. (1971). Testing for serial correlation in lest squared regression III, Biometrika 58, 1-19.
  9. Ljung, G. and Box, G. (1979). On a measure of lack of fit in time series models, Biometrika, 66, 265-270. https://doi.org/10.1093/biomet/66.2.265
  10. Park, Y. and Kim, K. (2003). Time Series Analysis I using SAS/ETS, Free Academy, Seoul.
  11. Park, Y. and Song, S. (1998). Economic Data Analysis using SAS/ETS, Jeong-Il press, Seoul.

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